by
Stewart, James; Redlin, Lothar; Watson, Saleem

Answer

30 years: $\$ 643.70$
15 years: $\$ 811.41$

Work Step by Step

We are given:
$A_{p}=80000, i= \frac{0.09}{12}=0.0075, n=30*12=360$
The present value of an annuity is given by:
$A_{p}=R \frac{1-(1+i)^{-n}}{i}$
We solve for $R$:
$R=\frac{iA_{p}}{1-(1+i)^{-n}}:$
$R=\frac{(0.0075)(80000)}{1-(1+0.0075)^{-360}}=\$ 643.70$
We re-calculate this for a 15 year period ($n=15*12=180$)
$R=\frac{0.0075*80000}{1-(1+0.0075)^{-180}}=\$ 811.41$